Convergence theorems with a stable limit law:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin
Akad.-Verl.
1993
|
| Edition: | 1. ed. |
| Series: | Mathematical research
70 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 199 S. |
| ISBN: | 3055014162 |
Staff View
MARC
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| 245 | 1 | 0 | |a Convergence theorems with a stable limit law |c by Gerd Christoph and Werner Wolf |
| 250 | |a 1. ed. | ||
| 264 | 1 | |a Berlin |b Akad.-Verl. |c 1993 | |
| 300 | |a 199 S. | ||
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Record in the Search Index
| _version_ | 1804120074288627712 |
|---|---|
| adam_text | Contents
1 Introduction 9
1.1 Main Definitions and Basic Properties of Stable Distributions ... 10
1.2 Examples of the Occurrence of Stable Laws 22
2 Properties of Pseudomoments and Their Generalizations 25
2.1 The Pseudomoments 25
2.2 The Difference Moments 29
2.3 The Integral Difference Moments 32
2.4 On the Existence of Integral Difference Moments 35
2.5 On the Difference between Characteristic Functions 39
2.6 Pseudomoments of Sums of Random Variables 41
2.7 Calculation of Pseudomoments 45
2.8 Further Extensions of Pseudomoments 52
3 Berry Esseen Type Inequalities with a Stable Limit Law 55
3.1 Weighted Sums of Independent Random Variables Attracted to Sta¬
ble Laws 55
3.2 Almost Sure Convergence of Weighted Sums 57
3.3 Inequalities of the Berry Esseen Type 59
3.4 Estimates in the Classical Summation 65
3.5 Another Method to Estimate the Distribution Function of Classical
Sums 68
3.6 A Series Criterion for the Rate to a Stable Law 74
3.7 Some Remarks on Necessary Conditions for a Certain Rate of Con¬
vergence 80
4 Asymptotic Expansions 87
4.1 Conditions on Characteristic Functions 89
4.2 Conditions on the Tails of the Distribution Functions 90
4.3 Formal Derivation of the Asymptotic Expansion 95
4.4 Limit Theorems with Asymptotic Expansions 99
8
4.5 Proof of Theorems on Asymptotic Expansion 107
4.6 On the Convergence of Sums of Reciprocals of Random Variables . 112
4.7 Asymptotic Expansion for Lattice Distributed Random Variables . 115
5 Non uniform Estimates in Asymptotic Expansions 121
5.1 Non uniform Estimates and Probabilities of Large Derivations ... 121
5.2 Main Results and Examples 126
5.3 The Truncation of Distribution Function 132
5.4 The Structure of the Proof of Theorem 5.2 134
5.5 Some Auxiliary Inequalities 135
5.6 Some Estimates for Characteristic Functions 139
5.7 The Proof of Theorem 5.2 144
6 Approximations of U Statistics by Stable Distributions 147
6.1 U Statistics 147
6.2 Uniform and Non Uniform Approximations of U Statistics by Stable
Distributions 148
6.3 Large Deviations for U Statistics 154
6.4 Theorems on Convergence to stable distributions 156
6.5 The Proofs of the Statements of Section 6.4 160
7 The Local Limit Problem for Stable Densities 167
7.1 The Local Central Limit Theorem 167
7.2 The Asymptotic Holder Continuity and the Local Limit Problem . 173
7.3 Density Approximations with Stable Densities 180
Bibliography 187
Index 200
|
| any_adam_object | 1 |
| author | Christoph, Gerd 1948- Wolf, Werner |
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| author_facet | Christoph, Gerd 1948- Wolf, Werner |
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| building | Verbundindex |
| bvnumber | BV005883598 |
| classification_rvk | QH 233 SK 800 |
| classification_tum | MAT 604f |
| ctrlnum | (OCoLC)246825670 (DE-599)BVBBV005883598 |
| discipline | Mathematik Wirtschaftswissenschaften |
| edition | 1. ed. |
| format | Book |
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| id | DE-604.BV005883598 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T16:36:18Z |
| institution | BVB |
| isbn | 3055014162 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-003684631 |
| oclc_num | 246825670 |
| open_access_boolean | |
| owner | DE-12 DE-91G DE-BY-TUM DE-739 DE-355 DE-BY-UBR DE-824 DE-945 DE-20 DE-634 DE-188 DE-706 |
| owner_facet | DE-12 DE-91G DE-BY-TUM DE-739 DE-355 DE-BY-UBR DE-824 DE-945 DE-20 DE-634 DE-188 DE-706 |
| physical | 199 S. |
| publishDate | 1993 |
| publishDateSearch | 1993 |
| publishDateSort | 1993 |
| publisher | Akad.-Verl. |
| record_format | marc |
| series | Mathematical research |
| series2 | Mathematical research |
| spelling | Christoph, Gerd 1948- Verfasser (DE-588)124307434 aut Convergence theorems with a stable limit law by Gerd Christoph and Werner Wolf 1. ed. Berlin Akad.-Verl. 1993 199 S. txt rdacontent n rdamedia nc rdacarrier Mathematical research 70 Wahrscheinlichkeitsverteilung (DE-588)4121894-2 gnd rswk-swf Stabile Verteilung (DE-588)4306935-6 gnd rswk-swf Stabilität (DE-588)4056693-6 gnd rswk-swf Konvergenz (DE-588)4032326-2 gnd rswk-swf Stabile Verteilung (DE-588)4306935-6 s DE-604 Stabilität (DE-588)4056693-6 s Wahrscheinlichkeitsverteilung (DE-588)4121894-2 s Konvergenz (DE-588)4032326-2 s Wolf, Werner Verfasser aut Mathematical research 70 (DE-604)BV000008585 70 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003684631&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Christoph, Gerd 1948- Wolf, Werner Convergence theorems with a stable limit law Mathematical research Wahrscheinlichkeitsverteilung (DE-588)4121894-2 gnd Stabile Verteilung (DE-588)4306935-6 gnd Stabilität (DE-588)4056693-6 gnd Konvergenz (DE-588)4032326-2 gnd |
| subject_GND | (DE-588)4121894-2 (DE-588)4306935-6 (DE-588)4056693-6 (DE-588)4032326-2 |
| title | Convergence theorems with a stable limit law |
| title_auth | Convergence theorems with a stable limit law |
| title_exact_search | Convergence theorems with a stable limit law |
| title_full | Convergence theorems with a stable limit law by Gerd Christoph and Werner Wolf |
| title_fullStr | Convergence theorems with a stable limit law by Gerd Christoph and Werner Wolf |
| title_full_unstemmed | Convergence theorems with a stable limit law by Gerd Christoph and Werner Wolf |
| title_short | Convergence theorems with a stable limit law |
| title_sort | convergence theorems with a stable limit law |
| topic | Wahrscheinlichkeitsverteilung (DE-588)4121894-2 gnd Stabile Verteilung (DE-588)4306935-6 gnd Stabilität (DE-588)4056693-6 gnd Konvergenz (DE-588)4032326-2 gnd |
| topic_facet | Wahrscheinlichkeitsverteilung Stabile Verteilung Stabilität Konvergenz |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003684631&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000008585 |
| work_keys_str_mv | AT christophgerd convergencetheoremswithastablelimitlaw AT wolfwerner convergencetheoremswithastablelimitlaw |